Physics in non-fixed spatial dimensions via random networks

• URL: http://arxiv.org/abs/2106.08911v4
• Date: Fri, 11 Mar 2022 12:32:07 GMT
• Title: Physics in non-fixed spatial dimensions via random networks
• Authors: Ioannis Kleftogiannis, Ilias Amanatidis
• Abstract summary: We study the quantum statistical electronic properties of random networks which inherently lack a fixed spatial dimension. We use tools like the density of states (DOS) and the inverse participation ratio(IPR) to uncover various phenomena. Our results imply that universal physics can manifest in physical systems irrespective of their spatial dimension.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the quantum statistical electronic properties of random networks which inherently lack a fixed spatial dimension. We use tools like the density of states (DOS) and the inverse participation ratio(IPR) to uncover various phenomena, such as unconventional properties of the energy spectrum and persistent localized states(PLS) at various energies, corresponding to quantum phases with with zero-dimensional(0D) and one-dimensional(1D) order. For small ratio of edges over vertices in the network $RT$ we find properties resembling graphene/honeycomb lattices, like a similar DOS containing a linear dispersion relation at the band center at energy E=0. In addition we find PLS at various energies including E=-1,0,1 and others, for example related to the golden ratio. At E=0 the PLS lie at disconnected vertices, due to partial bipartite symmetries of the random networks (0D order). At E=-1,1 the PLS lie mostly at pairs of vertices(bonds), while the rest of the PLS at other energies, like the ones related to the golden ratio, lie at lines of vertices of fixed length(1D order), at the spatial boundary of the network, resembling the edge states in confined graphene systems with zig-zag edges. As the ratio $RT$ is increased the DOS of the network approaches the Wigner semi-circle, corresponding to random symmetric matrices(Hamiltonians) and the PLS are reduced and gradually disappear as the connectivity in the network increases. Finally we calculate the spatial dimension $D$ of the network and its fluctuations, obtaining both integer and non-integer values and examine its relation to the electronic properties derived. Our results imply that universal physics can manifest in physical systems irrespectively of their spatial dimension. Relations to emergent spacetime in quantum and emergent gravity approaches are also discussed.

Related papers

• Neural Spacetimes for DAG Representation Learning [23.54420278189682]
  We propose a class of trainable deep learning-based geometries called Neural Spacetimes. We encode both graph edge weights in its spatial dimensions and causality in the form of edge directionality in its temporal dimensions. Our main theoretical guarantee is a universal embedding theorem, showing that any $k$-point DAG can be embedded into an NST with $1+mathcalO(log(k))$ distortion.
  arXiv  Detail & Related papers  (2024-08-25T16:26:55Z)
• Dipole-dipole interactions mediated by a photonic flat band [44.99833362998488]
  We study the photon-dipole interactions between emitters dispersively coupled to the photonic analogue of a flat band (FB) We show that the strength of such photon-mediated interactions decays exponentially with distance with a characteristic localization length. We find that the localization length grows with the overlap between CLSs according to an analytically-derived universal scaling law valid for a large class of FBs both in 1D and 2D.
  arXiv  Detail & Related papers  (2024-05-30T18:00:05Z)
• Quantum Chaos on Edge [36.136619420474766]
  We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension. While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
  arXiv  Detail & Related papers  (2024-03-20T11:31:51Z)
• Combinatorial quantum gravity and emergent 3D quantum behaviour [0.0]
  We review quantum gravity, an approach which combines Einstein's idea of dynamical geometry with Wheeler's "it from bit" hypothesis. In the 2D case, the geometric phase describes negative-curvature surfaces with two inversely related scales, an ultraviolet (UV) Planck length and an infrared (IR) radius of curvature. We obtain curved trajectories around massive particles also in 3D, representing the large-scale gravity interactions.
  arXiv  Detail & Related papers  (2023-11-29T10:54:51Z)
• Quantum Gauge Networks: A New Kind of Tensor Network [0.0]
  We introduce quantum gauge networks: a different kind of tensor network ansatz. A quantum gauge network (QGN) has a similar structure, except the Hilbert space dimensions of the local wavefunctions and connections are truncated. We provide a simple QGN algorithm for approximate simulations of quantum dynamics in any spatial dimension.
  arXiv  Detail & Related papers  (2022-10-21T17:59:00Z)
• Parity-time symmetric holographic principle [0.0]
  A spinless relativistic quantum particle traveling in (1+1)-dimensional space-time is simulated under a $mathcalPT$-symmetric Hamiltonian. Our work finds the application of $mathcalPT$-symmetric and non-Hermitian physics in quantum simulation.
  arXiv  Detail & Related papers  (2022-10-03T18:00:00Z)
• Ternary unitary quantum lattice models and circuits in $2 + 1$ dimensions [0.0]
  We extend the concept of dual unitary quantum gates to quantum lattice models in $2 + 1$ dimensions. We study ternary unitary four-particle gates, which are unitary in time and both spatial dimensions.
  arXiv  Detail & Related papers  (2022-06-03T10:53:49Z)
• Spectral embedding and the latent geometry of multipartite networks [67.56499794542228]
  Many networks are multipartite, meaning their nodes can be divided into partitions and nodes of the same partition are never connected. This paper demonstrates that the node representations obtained via spectral embedding live near partition-specific low-dimensional subspaces of a higher-dimensional ambient space. We propose a follow-on step after spectral embedding, to recover node representations in their intrinsic rather than ambient dimension.
  arXiv  Detail & Related papers  (2022-02-08T15:52:03Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• The Large $N$ Limit of icMERA and Holography [0.0]
  We compute the entanglement entropy in continuous icMERA tensor networks for large $N$ models at strong coupling. Our results constitute the first tensor network calculations at large $N$ and strong coupling simultaneously.
  arXiv  Detail & Related papers  (2021-07-28T10:14:47Z)
• Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits [62.997667081978825]
  We show that a controlled interaction with the environment may help to create a state, dubbed as em dark'', which is immune to decoherence. To encode quantum information in the dark states, they need to span a space with a dimensionality larger than one, so different states act as a computational basis. This approach offers new possibilities for storing, protecting and manipulating quantum information in open systems.
  arXiv  Detail & Related papers  (2020-02-01T15:57:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.